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| 184_notes:e_b_summary [2021/06/16 22:26] – [Static Electric Fields] bartonmo | 184_notes:e_b_summary [2021/06/16 22:36] (current) – bartonmo |
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| Now that we have the basics down for both electric and magnetic fields, we will start to consider the cases where charges feel an effect from both electric and magnetic interactions. (We will also return to this idea again at the end of the course.) This page of notes serves as a reminder of some of the important concepts about static electric fields and static magnetic fields that we will be building on for the rest of the semester. | Now that we have the basics down for both electric and magnetic fields, we will start to consider the cases where charges feel an effect from both electric and magnetic interactions. (We will also return to this idea again at the end of the course.) This page of notes serves as a reminder of some of the important concepts about static electric fields and static magnetic fields that we will be building on for the rest of the semester. |
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| ==== Static Electric Fields ==== | ===== Static Electric Fields ===== |
| In the beginning of the semester, we talked about how [[184_notes:charge|electric charges]] created electric fields. We talked specifically about the [[184_notes:pc_efield|electric field from point charges]] which points radially outwards for positive charges (or radially inward for negative charges). We then used both computational methods (VPython code) and analytical methods (integration) to find the electric field for [[184_notes:line_fields|lines of charge]], [[course_planning:184_projects:f18_project_3|planes of charge]], and [[184_notes:dist_charges|volumes of charge (cylinders and spheres)]]. In each of these cases, we found that the electric field would still point away from positive charges and toward negative charges. | In the beginning of the semester, we talked about how [[184_notes:charge|electric charges]] created electric fields. We talked specifically about the [[184_notes:pc_efield|electric field from point charges]] which points radially outwards for positive charges (or radially inward for negative charges). We then used both computational methods (VPython code) and analytical methods (integration) to find the electric field for [[184_notes:line_fields|lines of charge]], [[course_planning:184_projects:f18_project_3|planes of charge]], and [[184_notes:dist_charges|volumes of charge (cylinders and spheres)]]. In each of these cases, we found that the electric field would still point away from positive charges and toward negative charges. |
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| The [[184_notes:pc_force|electric force]] was then defined by how a charge would interact with an electric field: $\vec{F}_{E}=q\vec{E}$. Because the charge is a scalar value, the electric force will always point either in the same direction as the electric field (for positive charges) or opposite the electric field (for negative charges), which will cause the charge to accelerate. Since the path that the charges follow is in the same direction as the electric force, we can [[184_notes:pc_vefu|relate the electric force]] to a change in [[184_notes:pc_energy|electric potential energy]] or to a change in [[184_notes:pc_potential|electric potential.]] | The [[184_notes:pc_force|electric force]] was then defined by how a charge would interact with an electric field: $\vec{F}_{E}=q\vec{E}$. Because the charge is a scalar value, the electric force will always point either in the same direction as the electric field (for positive charges) or opposite the electric field (for negative charges), which will cause the charge to accelerate. Since the path that the charges follow is in the same direction as the electric force, we can [[184_notes:pc_vefu|relate the electric force]] to a change in [[184_notes:pc_energy|electric potential energy]] or to a change in [[184_notes:pc_potential|electric potential.]] |
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| ==== Static Magnetic Fields ==== | ===== Static Magnetic Fields ===== |
| In contrast to electric fields, we found that a [[184_notes:moving_q|moving charge created a magnetic field]] that was **perpendicular** to motion of the moving charge. This meant that the magnetic field pointed circularly around a moving charge, which we were able to determine using the [[184_notes:rhr|right hand rule]]. Again, we used computational and analytical methods to show that the [[184_notes:b_current|magnetic field from a current]] also followed a similar pattern. From these basic sources, we could then extend to the magnetic field from [[184_notes:b_shapes|current loops]], from [[184_notes:perm_mag|bar magnets]], and (briefly) from [[184_notes:b_shapes|solenoids]]. | In contrast to electric fields, we found that a [[184_notes:moving_q|moving charge created a magnetic field]] that was **perpendicular** to motion of the moving charge. This meant that the magnetic field pointed circularly around a moving charge, which we were able to determine using the [[184_notes:rhr|right hand rule]]. Again, we used computational and analytical methods to show that the [[184_notes:b_current|magnetic field from a current]] also followed a similar pattern. From these basic sources, we could then extend to the magnetic field from [[184_notes:b_shapes|current loops]], from [[184_notes:perm_mag|bar magnets]], and (briefly) from [[184_notes:b_shapes|solenoids]]. |
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